The Distribution of the Instrumental Variables Estimator and its T-Ratiowhen the Instrument is a Poor One

24 Pages Posted: 27 Jun 2007 Last revised: 11 Sep 2010

Date Written: September 1988

Abstract

When the instrumental variable is a poor one, in the sense of being weakly correlated with the variable it proxies, the small sample distribution of the IV estimator is concentrated around a value that is inversely related to the feedback in the system and which is often further from the true value than is the plim of OLS. The sample variance of residuals similarly becomes concentrated around a value which reflects feedback and not the variance of the disturbance. The distribution of the t-ratio reflects both of these effects, stronger feedback producing larger t-ratios. Thus, in situations where OLS is badly biased, a poor instrument will lead to spurious inferences under IV estimation with high probability, and generally perform worse than OLS.

Suggested Citation

Nelson, Charles R. and Startz, Richard, The Distribution of the Instrumental Variables Estimator and its T-Ratiowhen the Instrument is a Poor One (September 1988). NBER Working Paper No. t0069, Available at SSRN: https://ssrn.com/abstract=994511

Charles R. Nelson (Contact Author)

Dept of Economics ( email )

Box 353330
Seattle, WA 98195-3330
United States

Richard Startz

UCSB ( email )

Department of Economics
University of California
Santa Barbara, CA 93106-9210
United States
805-893-2895 (Phone)

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
24
Abstract Views
1,224
PlumX Metrics